The present invention relates to tracking phase in a vestigial sideband (“VSB”) receiver. The ATSC digital television (“DTV”) terrestrial transmission standard was adopted in 1996. Since then, several generations of receivers have been developed, which attempt to improve the reception performance of a previous generation of receivers.
In an ATSC DTV transmission system, data is transmitted in frames 10 as shown in FIG. 1. Each frame includes 2 fields 15 and 20; each field includes 313 segments; and each segment includes 832 symbols for a total of 260,416 symbols per field. The first four symbols in each segment are segment sync symbols 25 having the sequence [+5, −5, −5, +5].
The first segment in each field is a field sync segment 30 as shown in FIG. 2. The field sync segment 30 includes a segment sync 35, a 511 symbol pseudo noise (“PN511”) sequence 40, a 63 symbol pseudo noise (“PN63”) sequence 45, a second PN63 sequence 50, and a third PN63 sequence 55, which are followed by 24 symbols 60 indicating that the transmission mode is 8VSB. In alternating fields, the three PN63 sequences are the same. In the remaining fields, the first and third PN63 sequences are the same, while the second PN63 sequence is inverted. In either case, the first 728 symbols of the segment are a priori known to the receiver and may be used for equalizer training. Following the first 728 symbols are 92 symbols 65 including mode and reserved fields. All of the symbols are from the set {+5 −5}. The last 12 symbols 70 of this segment are precode symbols and are from the set {−7 −5 −3 −1 +1 +3 +5+7} and are duplicates of the last 12 symbols of the previous data field.
The subsequent 312 segments of the field are referred to as data segments 75 and include 828 trellis encoded symbols 80 following the four segment sync symbols 35, as shown in FIG. 3. The trellis encoded symbols 80 are encoded by, for example, a 12-phase trellis encoder, which results in 8 level symbols from the set {−7 −5 −3 −1 +1 +3 +5 +7}.
FIG. 4 illustrates a VSB transmitter 100. In the transmitter 100, data is randomized in a randomizer 105, Reed-Solomon byte wise encoded in a Reed-Solomon encoder 110, and then byte interleaved in an interleaver 115. The data is trellis encoded by a 12-phase trellis encoder 120. A frame formatter 125 adds the segment sync symbols and the field sync symbols to the trellis encoded data at the appropriate times to create the data frame structure of FIG. 1. A pilot carrier module 130 then adds a fixed DC level to each symbol.
A modulator 135 incorporates root raised cosine pulse shaping (described below) and modulates the signal for RF transmission as an 8VSB signal with a symbol rate of 10.76 MHz. The 8VSB signal differs from commonly used linear modulation methods such as quadrature-amplitude modulation (“QAM”) in that the 8VSB symbols are real, but have a pulse shape that is complex, with only the real part of the pulse having a Nyquist shape.
FIG. 5 is a diagram of an 8VSB receiver 200. A tuner 205 and demodulator 210 demodulate the RF signal to baseband before timing and synchronization recovery in a sync and timing recovery module 215. The data is then match filtered in a matched filter 220, equalized in an equalizer 225, and sent through a phase tracking module 230, trellis decoder 235, de-interleaver 240, Reed-Solomon decoder 245, and de-randomizer 250. During the process of down converting a VSB signal, the tuner 205 adds phase noise to the signal, which affects the input to the matched filter 220. In a well-designed frequency and phase locked loop (“FPLL”) carrier recovery system, the receiver 200 is able to lock on to the incoming frequency in addition to removing much of the phase noise introduced by the tuner 205. However, the phase noise which is outside of the bandwidth of the FPLL passes through to the remaining components in the VSB receiver 200.
The channel between the transmitter 100 and receiver 200 is viewed in its baseband equivalent form to accurately describe the signal at the input to the phase tracker 230. The baseband signal model assumes that the carrier frequency and symbol clock frequency were recovered in the sync and timing recovery module 215. The transmitted signal has a root raised cosine spectrum with a nominal bandwidth of 5.38 MHz and an excess bandwidth of 11.5% centered at one fourth of the symbol rate (i.e., 2.69 MHz). Thus, the transmitted pulse shape q(t) is complex and is given by EQN. 1.q(t)=ejπFst/2qRRC(t)  EQN. 1where Fs is the symbol frequency, and qRRC(t) is a real square root raised cosine pulse with an excess bandwidth of 11.5% of the channel. The pulse q(t) is referred to as the “complex root raised cosine pulse.” For the 8VSB system, the transmitter pulse shape q(t) and the receiver matched filter pulse shape q*(−t) are identical since q(t) is conjugate-symmetric. Thus, the raised cosine pulse p(t), referred to as the “complex raised cosine pulse,” is given by EQN. 2.p(t)=q(t)*q*(−t)  EQN. 2where * denotes convolution, and * denotes complex conjugation.
The transmitted baseband signal of data rate 1/T symbols/sec is represented as EQN. 3.
                              z          ⁡                      (            t            )                          =                              ∑            n                    ⁢                                    s              ⁡                              (                n                )                                      ⁢                          q              ⁡                              (                                  t                  -                  nT                                )                                                                        EQN        .                                  ⁢        3            where {s(n)εA≡{a1, . . . a8}⊂R1} is the transmitted data sequence, which is a discrete 8-ary sequence taking values on the real 8-ary alphabet A. The physical channel between the transmitter 100 and receiver 200 is denoted as c(t) and is mathematically modeled using EQN. 4.
                              c          ⁡                      (            t            )                          =                              ∑                          n              =                              -                                  L                  ha                                                                    L              hc                                ⁢                                    β              n                        ⁢                          δ              ⁡                              (                                  t                  -                                      τ                    n                                                  )                                                                        EQN        .                                  ⁢        4            where {βn}⊂C1, Lha and Lhc are the maximum number of anti-causal and causal multipath components, respectively, τn is multipath delay, and δ(t) is the Dirac delta function.
Because the matched filter 220 is a relatively short duration filter, the phase noise, θ(t), is assumed to be approximately constant for the entire filter. Therefore, the matched filter output sampled at the symbol rate can be approximated with the expression in EQN. 5,
                                          r            mf                    ⁡                      (            k            )                          ≈                                            ⅇ                              ⅈθ                ⁡                                  (                  k                  )                                                      ⁢                                          ∑                n                            ⁢                                                s                  ⁡                                      (                    n                    )                                                  ⁢                                  h                  ⁡                                      (                                          k                      -                      n                                        )                                                                                +                      n            ⁡                          (              k              )                                                          EQN        .                                  ⁢        5            where the overall channel impulse response is given by
                              h          ⁡                      (            k            )                          =                                                                                             p                  ⁡                                      (                    t                    )                                                  *                                  c                  ⁡                                      (                    t                    )                                                                                                    t              =              kT                                =                                    ∑                              n                =                                  -                                      L                    ha                                                                              L                hc                                      ⁢                                                                                                 β                    n                                    ⁢                                      p                    ⁡                                          (                                              t                        -                                                  τ                          n                                                                    )                                                                                                                  t                =                kT                                                                        EQN        .                                  ⁢        6            and the complex noise term after the matched filter is given byn(k)=(η(t)eiθ(t))*q*(−t)|t=kT  EQN. 7with η(t) being a zero-mean white Gaussian noise process with spectral density σn2 for each real and imaginary part.
The real part of the matched filter output is then input into the real equalizer 225. The phase noise is assumed to be relatively constant over the duration of the equalizer impulse response (i.e. θ(k−n)≈θ(k)∀|n|<M, where 2M+1 is the length of the equalizer filter, gEQ(k)), and the equalizer 225 is assumed to effectively remove the intersymbol interference (“ISI”) from the channel, which results inRe{c(k)*p(k)*geq(k)}=δ(k)  EQN. 8
Therefore, the equalizer output, xR(k), can be expressed as
                                                                                                              x                    R                                    ⁡                                      (                    k                    )                                                  =                                                      Re                    ⁢                                          {                                                                        ⅇ                                                      ⅈθ                            ⁡                                                          (                              k                              )                                                                                                      ⁡                                                  (                                                                                    s                              ⁡                                                              (                                k                                )                                                                                      +                                                          ⅈ                              ⁢                                                                                                                          ⁢                                                              H                                ′                                                            ⁢                                                              {                                                                  s                                  ⁡                                                                      (                                    k                                    )                                                                                                  }                                                                                                              )                                                                    }                                                        +                                                            n                      R                      ′                                        ⁡                                          (                      k                      )                                                                                                                                              =                                                      cos                    ⁢                                                                                  ⁢                                          (                                              θ                        ⁡                                                  (                          k                          )                                                                    )                                        ⁢                                          s                      ⁡                                              (                        k                        )                                                                              -                                                            sin                      ⁡                                              (                                                  θ                          ⁡                                                      (                            k                            )                                                                          )                                                              ⁢                                          v                      ⁡                                              (                        k                        )                                                                              +                                                            n                      R                      ′                                        ⁡                                          (                      k                      )                                                                                                          ⁢                                  ⁢        where                            EQN        .                                  ⁢        9                                          v          ⁡                      (            k            )                          =                              H            ′                    ⁢                      {                          s              ⁡                              (                k                )                                      }                    ⁢                                          ⁢          and                                    EQN        .                                  ⁢        10                                                      n            R            ′                    ⁡                      (            k            )                          =                  Re          ⁢                      {                          n              ⁡                              (                k                )                                      }                    *                                    g              eq                        ⁡                          (              k              )                                                          EQN        .                                  ⁢        11            H′ { } is herein referred to as the pseudo-Hilbert transform and is the imaginary portion of the raised cosine pulse defined in EQN. 2. Therefore, using the pseudo-Hilbert transform, H′ { }, the imaginary part of the equalizer output is generated as shown below in EQN. 12.
                                                        x              I                        ⁡                          (              k              )                                ≡                                    H              ′                        ⁢                          {                                                x                  R                                ⁡                                  (                  k                  )                                            }                                      =                                                            H                ′                            ⁢                              {                                                      cos                    ⁡                                          (                                              θ                        ⁡                                                  (                          k                          )                                                                    )                                                        ⁢                                      s                    ⁡                                          (                      k                      )                                                                      }                                      -                                          H                ′                            ⁢                              {                                                      sin                    ⁡                                          (                                              θ                        ⁡                                                  (                          k                          )                                                                    )                                                        ⁢                                      H                    ′                                    ⁢                                      {                                          s                      ⁡                                              (                        k                        )                                                              }                                                  }                                      +                                          H                ′                            ⁢                              {                                                      n                    R                    ′                                    ⁡                                      (                    k                    )                                                  }                                              ≈                                                    cos                ⁡                                  (                                      θ                    ⁡                                          (                      k                      )                                                        )                                            ⁢                              v                ⁡                                  (                  k                  )                                                      +                                          sin                ⁡                                  (                                      θ                    ⁡                                          (                      k                      )                                                        )                                            ⁢                              s                ⁡                                  (                  k                  )                                                      +                                          H                ′                            ⁢                              {                                                      n                    R                    ′                                    ⁡                                      (                    k                    )                                                  }                                                                        EQN        .                                  ⁢        12            where it is again assumed that the phase noise is relatively constant over a short duration filter, making cos(θ(k)) and sin(θ(k)) multiplicative constants. An important property of a Hilbert transform is that H{H{x(k)}}=−x(k). Although not strictly true for the pseudo-Hilbert transform, it is noted that the pseudo-Hilbert transform retains this property in an approximate sense, H′{H′{x(k)}}≈−x(k). The input into the phase tracker is then expressed below as EQN. 13.x(k)≡xR(k)+ixI(k)≈eiθ(k)[s(k)+iv(k)]+nR′(k)+iH′{nR′(k)}  EQN. 13
A diagram of a decision-directed (“DD”) phase tracking loop 300 for quadrature amplitude modulation (“QAM”) is illustrated in FIG. 6. All indices shown refer to the symbol rate. The complex input, x(k), 305 is de-rotated by the current phase estimate, {circumflex over (θ)}(k), 310. The resultant de-rotated signal, y(k), 315 is input into a decision device 320 (e.g., a slicer) and an error generator 325. The error generator 325 uses the de-rotated signal, y(k), 315 and complex symbol decision, ĉ(k), 330 to generate an instantaneous error estimate, e(k), 335. The instantaneous error estimate 335 is low-pass filtered in a low-pass filter 340 to generate the phase estimate 310. A look-up table (“LUT”) is then used to compute e−iθ(k) to de-rotate the received signal.
One measure of the performance of the error generator 325 is an S-curve. The S-curve is defined as the expectation of an error signal for a fixed value of the difference between the actual phase noise and the phase estimate, ψ=θ−{circumflex over (θ)}. That is,S(ψ)=E{e(k)|ψ}  EQN. 14
Another measure of the performance of the error generator 325 is variance. A good error generator's S-curve is linear about the origin and has a low variance. Thus, for unbiased error generators, the instantaneous error estimate is expressed using EQN. 15.e(k)=S(θ(k)−{circumflex over (θ)}(k))+N(k)≈A(θ(k)−{circumflex over (θ)}(k))+N(k)  EQN. 15where A is the slope of the S-curve about the origin. The S-curve and slope A are obtained experimentally. The bandwidth of the phase tracking loop 300 is calculated using EQN. 16.
                              B          L                =                              1            T                    ·                                    γ              ⁢                                                          ⁢              A                                      2              ⁢                              (                                  2                  -                                      γ                    ⁢                                                                                  ⁢                    A                                                  )                                                                        EQN        .                                  ⁢        16            Therefore, with a known S-curve slope for the error generator 325, the bandwidth of the phase tracking loop is adjusted using the parameter of the loop filter, γ, and changes based on the specifications of the tuner 205 used.